## L Shape Retaining Wall Design

Effects of actions

'Effects of actions' (or 'action effects') is a general term denoting internal forces, moments, stresses, and strains in structural members — plus the deflection and rotation of the whole structure. [en 1990 §1.5.3.2]

For most structural designs, verification of limit state STR involves action effects that are independent of the strength of the structural materials (see Chapter 2). However, in many geotechnical designs, verification of the STR

and GEO limit states involves effects of actions that depend upon the strength of the ground.

internal stresses settlement earth pressure Figure 6.2. Actions (left) and effects (right) for L-shaped gravity retaining wall

For example, Figure 6.2 shows a retaining wall supporting loose soil and an imposed uniform surcharge (q). The earth pressures acting behind the wall produce a horizontal sliding force HE (an action effect) given by:

where h is the wall's height; y and 9 the soil's self-weight and angle of shearing resistance; and Ka is Rankine's active earth pressure coefficient.

This simple example illustrates why the definition of design effects of actions given in the head Eurocode:

has to be revised for geotechnical design to:

where Fd = design actions applied to the structure; Xd = design material properties; and ad = design dimensions of the structure. (The notation E{...} denotes a function of the enclosed parameters and usually involves multiple parameters of each type listed.)

Put simply, in structural design, effects of actions are generally a function of actions and dimensions only; whereas, in geotechnical design, effects of actions are typically a function of actions, dimensions, and the strength of the ground.

The inclusion of Xd in the equation for Ed adds considerable complexity to designs involving geotechnical actions and is one of the reasons for the diversity of design methods used in geotechnical design.

6.1.2 Resistance

'Resistance' is defined as the:

capacity of a [member or] component, or cross-section of a [member or] component of a structure, to withstand actions without mechanical failure

(The words in brackets are omitted in Eurocode 7's definition. The absence of the word 'ground' from either definition appears to be an error - unless we regard the ground as a component of the structure.)

For most structural designs, verification of limit state STR involves resistances that are independent of actions (see Chapter 2). However, in many geotechnical designs, verification of the STR and GEO limit states involves resistances that depend upon actions.

For example, Figure 6.3 illustrates the sliding resistance HR of the retaining wall shown previously in Figure 6.2:

where the resistance is a function of the wall's dimensions (h and b), the self-weight of the soil (y) - and the strength of the soil-structure interface (5, which itself is a function of the soil's drained angle of shearing resistance 9).

Again this example illustrates why the definition of resistance given in the head Eurocode:

YRd has to be revised for geotechnical design to:

d~ Yr where Fd, Xd, and ad are as defined earlier. Here, R{...} denotes a function of the enclosed parameters and YRd = YR = a partial factor on resistance.

In simple terms, in structural design, resistances are generally a function of material strengths and dimensions only; whereas, in geotechnical design, resistances are typically a function of material strengths, dimensions, and actions, including the self-weight of the ground.

Once again, the inclusion of Fd in the equation for Rd adds considerable complexity to designs involving geotechnical materials and is another reason for the diversity of design methods used in geotechnical design.

6.2 Introducing reliability into the design

'The word safety is encompassed in the Eurocodes in the word reliability.'2

Reliability can be introduced into the design in a number of ways, through the application of suitable partial factors or tolerances, as illustrated in Figure 6.4.

In the top half of this diagram, there are three 'channels' that lead into the calculation model: one for actions (left), another for geometrical parameters (centre), and a third for materials properties (right). Certain material properties, such as weight density, have a direct influence on actions, whereas other material properties, such as strength, do not (they do, however, influence the action effects).

Verification occurs in the bottom third of the diagram: the calculation model provides values for effects of actions (left) and resistance (right), which are compared against each other (in the centre).

Partial factors (or tolerances) can be applied to one or more of:

• material properties (X) and/or resistances (R)

• geometrical parameters (a)

These factors/tolerances are shown on Figure 6.4 in the wavy boxes.

6.2.1 Actions and effects

The calculation of design effects of actions follows the route shown in the left hand channel of Figure 6.4:

Characteristic actions ^ Representative actions ^ Design actions ^ Design effects of actions

Characteristic actions Fk are calculated according to the rules of Eurocode 1. Characteristic self-weights are calculated as the product of a material's characteristic weight density Yk and its nominal dimensions anom (see Chapter 2):

Representative actions Frep are obtained from characteristic actions by multiplying by correlation factors ^ < 1.0 (where ^ = 1.0 for permanent actions, see Chapter 2):

Frep = WFk

The total design action Fd is then obtained as the sum of all the representative actions multiplied by their corresponding partial factors yf $ 1.0:

The design effects of actions are then obtained from:

Figure 6.5 shows the relative magnitude of actions as appropriate combination factors (1.0 or and partial factors (yg and yq) are applied to them. The diagram assumes arbitrary values for the permanent, leading variable, and accompanying variable actions (G, Q1, and Qi respectively). The arrow denotes where design actions enter the calculation model.

Aclions

Effects

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